1. Field of the Invention
The present invention relates to petroleum reservoir exploration and development, and more particularly to petroleum reservoir imaging. The invention relates to a history matching method for a geological model representative of an underground reservoir which respects average proportions of lithologic facies. Constructing images representative of the subsoil and compatible with data measured in wells and/or the entire reservoir being studied allows reservoirs to be developed.
2. Description of the Prior Art
Studying a petroleum field requires constructing models referred to as “geological models” in a broad sense. These models, which are computer based, are well known and widely used in the petroleum industry, allow for example determination of many technical parameters relative to prospecting, study or development of a hydrocarbon reservoir. In fact, these geological models are representative of structures of reservoirs and of the behavior thereof. It is possible to determine which zones are the most likely to contain hydrocarbons, the zones in which it can be interesting/necessary to drill an injection well in order to enhance hydrocarbon recovery, the type of tools to use and the properties of the fluids used and recovered, etc. These interpretations of geological models in terms of “technical development parameters” are well known, even though new methods are regularly developed. It is crucial, in the petroleum field, to construct a model as precise as possible. Integration of all the available data is therefore essential.
A geological model is a model of the subsoil, representative of both the structure and the behavior thereof. Generally, this type of model is represented in a computer and is referred to as a numerical model. In two dimensions (2D), the model is referred to as a map. Thus, a map corresponds to an image of pixels with each pixel containing information relative to the behavior of the subsoil being studied (a petroleum reservoir for example). These pixels correspond to a precise geographical position and are identified by coordinates. When values are assigned to a pixel, by simulation for example, reference is made to a simulation point. The representative image (map or model) is generated on any support (paper, computer screen, etc.).
Petroleum reservoirs are generally highly heterogeneous and fractured porous media. Modelling a reservoir, that is constructing a geological model representative of the reservoir, requires construction methods referred to as “probabilistic” due to the limitation of available information (limited number of wells, etc.). The geological models constructed from these probabilistic methods are therefore referred to as “stochastic models”. Construction of a stochastic reservoir model first has to depend on the environment of the geological deposit, which allows representation of the major heterogeneities controlling the flow of fluids. A model then has to be constrained by quantitative data such as core data, log data and seismic data, which further increases the reliability of the model for production prediction. Thus, geostatistical modelling is used to construct geological models that best respect the available static data (well data, seismic data, etc.), that is the time-invariant data directly linked with the modelled properties.
In order to obtain the best possible image of the reservoir, it is necessary, in addition to static data, to integrate dynamic data. The dynamic data are indirectly linked with the modelled properties and they are time-dependent. These data are, for example, oil flow rates measured in wells, tracer concentrations or successive repeat seismic acquisition surveys.
The integration of production and seismic data in a reservoir model is a process referred to as “history matching” of a geological model. The principle modifies the initial geological model iteratively until the simulated dynamic behavior is as close as possible to the observed dynamic behaviour. This problem is solved by adjusting some parameters of the geological model by minimizing a function referred to as objective function, which quantifies the difference between the dynamic data and the simulated corresponding responses.
Many techniques have been developed in the past years for modifying the geological model while preserving coherence with respect to the static observations. A geological model contains information on the petrophysical properties. The available static data are used to define random functions for each petrophysical property. A representation of the spatial distribution of a petrophysical property is a realization of a random function. The perturbation techniques allow modification of a realization of a random function while ensuring the fact that the perturbed realization is also a realization of this random function.
Examples of these perturbation techniques are the pilot point method developed by RamaRao et al. (1995) and Gomez-Hernandez et al. (1997), as well as the gradual deformation method provided by Hu (2000). These methods allow modification of the spatial distribution of the heterogeneities.    RamaRao, B. S; Lavenue, A. M.; Marsilly, G. de; Marietta, M. G.; Pilot Point Methodology for of an Ensemble of Conditionally Simulated Transmissivity Fields. 1. Theory and Computational Experiments. WRR, 1995, vol. 31 (3), 475-493.    Gomez-Hernandez, J., Sahuquillo, A., et Capilla, J. E., 1997, Stochastic Simulation of Transmissivity Fields Conditional to Both Transmissivity and Piezometric Data, 1. Theory, J. of Hydrology, 203, 162-174.    Hu, L-Y., 2000, Gradual Deformation and Iterative Calibration of Gaussian-related Stochastic Models, Math. Geol., 32(1), 87-108.
A particularly sensitive property for the development of a reservoir is the lithologic facies proportion. In fact, lithologic facies proportions can have a major impact on the dynamic behavior of an oil field. They can be identical over the entire domain (stationary case) or vary depending on the position (non-stationary case). What is referred to as lithologic facies is a property of a rock. For example, the lithologic facies can refer to the geological nature of the rock (clay, sandstone, limestone, etc.), to its porosity type (unconsolidated and very porous rock; low-porosity rock, etc.), or to the nature of the fluid trapped in the pores (brine, oil, gas, etc.).
Usually, well data are used to determine one or more vertical facies proportion curves. These curves give the probability of occurrence of each facies as a function of depth. These curves are then used to construct, notably from kriging techniques, a facies proportion matrix that determines, for each cell of the grid representative of the reservoir, the occurrence probabilities of the various facies. These probabilities constrain the spatial distribution of the facies in the geological model.
Hoffman and Caers (2007) provide a method allowing increasing or decreasing the proportion of the various facies according to results if the simulated dynamic production. This method complements the probability perturbation method (Hoffman and Caers, 2005) and it cannot be used alone.
Hoffman B. T., and Caers, J., History Matching by Jointly Perturbing Local Facies Proportions and Their Spatial Distribution: Application to a North Sea reservoir, Journal of Petroleum Science and Engineering 57 (2007) 257-272.    Hoffman B. T., and Caers, J., Regional Probability Perturbation for History Matching, J. Pet. Sci. Eng. 46, 53-71.
Another approach proposed by Liu and Oliver (2004) modifies the amounts of the various facies by acting directly upon the truncation thresholds used in the pluri-Gaussian method. The pluri-Gaussian method is a conventional known method, for generating a facies realization.    Liu, N. and Oliver, D. S., Automatic History Matching of Geologic Facies, SPE 84594, Proceeding of the 2003 SPE Annual, Technical Conference and Exhibition, SPE Journal, 9(4): 1-15, 2004.    Le Loc'h G. and Galli, A., 1997: Truncated Plurigaussian method: Theoretical and Practical Points of View. Geostatistics Wollongong '96, E. Y. Baafi and N. A. Schofields eds, Kluwe, p. 211-222.
Finally, another method is described in French Patent 2,914,434. It is a parameterization method that modifies the ratio of the average proportion over a zone of a facies association in relation to a facies selection.